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A numerical method using implicit surface representations is proposed to solve the linearized Poisson-Boltzmann equations that arise in mathematical models for the electrostatics of molecules in solvent. The proposed method used an implicit…

Numerical Analysis · Mathematics 2018-04-04 Yimin Zhong , Kui Ren , Richard Tsai

First-principles particle-in-cell (PIC) simulation is a powerful tool for understanding plasma behavior, but this power often comes at great computational expense. Artificially reducing the ion/electron mass ratio is a time-honored practice…

Plasma Physics · Physics 2022-01-14 Gregory R. Werner , Scott Robertson , Thomas G. Jenkins , Andrew M. Chap , John R. Cary

Relativistic strongly magnetized plasmas are produced in laboratories thanks to state-of-the-art laser technology but can naturally be found around compact objects such as neutron stars and black holes. Detailed studies of the behaviour of…

Plasma Physics · Physics 2017-05-24 J. Pétri

We present an explicit temporal discretization of particle-in-cell schemes for the Vlasov equation that results in exact energy conservation when combined with an appropriate spatial discretization. The scheme is inspired by a simple,…

Numerical Analysis · Mathematics 2024-11-15 Lee F. Ricketson , Jingwei Hu

Laboratory plasmas in open magnetic geometries can be found in many different applications such as (1) Scrape-Of-Layer (SOL) and divertor regions in toroidal confinement fusion devices (\approx1-10^2\hspace{1mm}\mathrm{eV}), (2) linear…

Plasma Physics · Physics 2022-02-09 Atul Kumar , J. F. Caneses Marin

The simulation of problems in kinetic plasma physics are often challenging due to strongly coupled phenomena across multiple scales. In this work, we propose a wavelet-based coarse-grained numerical scheme, based on the framework of…

Computational Physics · Physics 2016-10-05 Paul Cazeaux , Jan S. Hesthaven

We present in this work the implementation of the Energy Conserving Semi-Implicit Method in a parallel code called ECsim. This new code is a three-dimensional, fully electromagnetic particle in cell (PIC) code. It is written in C/C++ and…

Computational Physics · Physics 2018-07-04 Diego Gonzalez-Herrero , Elisabetta Boella , Giovanni Lapenta

We introduce a Galilean electromagnetic particle-in-cell (GEM-PIC) algorithm, which transforms the full set of Maxwell equations and the Vlasov equation into the boosted coordinates. This approach preserves the electromagnetic structure of…

Plasma Physics · Physics 2026-05-21 Alexander Pukhov , Nina Elkina , Tom Wilson

JAX-in-Cell is a fully electromagnetic, multispecies, and relativistic 1D3V Particle-in-Cell (PIC) framework implemented entirely in JAX. It provides a modern, Python-based alternative to traditional PIC frameworks. It leverages…

Plasma Physics · Physics 2025-12-16 Longyu Ma , Rogerio Jorge , Hongke Lu , Aaron Tran , Christopher Woolford

In simulations of partial differential equations using particle-in-cell (PIC) methods, it is often advantageous to resample the particle distribution function to increase simulation accuracy, reduce compute cost, and/or avoid numerical…

There are many interesting physical processes which involve the generation of high density plasmas in large volumes. However, when modeling these systems numerically, the large densities and volumes present a significant computational…

Computational Physics · Physics 2007-05-23 A. E. Schulz , A. D. Greenwood , K. L. Cartwright , P. J. Mardahl

The Particle-In-Cell (PIC) method for plasma simulation tracks particle phase space information using particle and grid data structures. High computational costs in 2D and 3D device-scale PIC simulations necessitate parallelization, with…

Computational Physics · Physics 2025-06-27 Libn Varghese , Bhaskar Chaudhury , Miral Shah , Mainak Bandyopadhyay

Particle-in-cell codes are the most widely used simulation tools for kinetic studies of ultra-intense laser-plasma interactions. Using the motion of a single electron in a plane electromagnetic wave as a benchmark problem, we show…

Plasma Physics · Physics 2021-04-07 Kavin Tangtartharakul , Guangye Chen , Alexey Arefiev

Particle-in-cell (PIC) is the most used algorithm to perform self-consistent tracking of intense charged particle beams. It is based on depositing macro-particles on a grid, and subsequently solving on it the Poisson equation. It is well…

Accelerator Physics · Physics 2016-01-27 Frederik Kesting , Giuliano Franchetti

Large-scale simulations of plasmas are essential for advancing our understanding of fusion devices, space, and astrophysical systems. Particle-in-Cell (PIC) codes have demonstrated their success in simulating numerous plasma phenomena on…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-07-05 Steven W. D. Chien , Jonas Nylund , Gabriel Bengtsson , Ivy B. Peng , Artur Podobas , Stefano Markidis

High-power magnetically shielded Hall thrusters have recently emerged to meet the needs of the next-generation space missions. Even though a few such thrusters are currently undergoing their late-stage development campaigns, many unanswered…

A modification of the implicit algorithm for particle-in-cell simulations proposed by Petrov and Davis [2011] is presented. The original lattice arrangement is not inherently divergence-free, possibly leading to unphysical results. This…

Computational Physics · Physics 2012-12-21 Andreas Kempf , Urs Ganse , Patrick Kilian , Felix Spanier

We take issue with the conclusions in the recent publication by Savard et al. In the study, the authors implement a fully nonlinear charge- and energy-conserving implicit particle-in-cell method (ECC-IPIC), and use it to study the impact of…

Plasma Physics · Physics 2026-03-04 Luis Chacon , Guangye Chen , Lee Ricketson

Based on the particle-in-cell (PIC) plasma simulation method, the speed-limited PIC (SLPIC) method delivers faster kinetic plasma simulation in cases where the particle distributions evolve slowly compared with the maximum stable PIC…

Computational Physics · Physics 2019-01-09 Gregory R. Werner , Thomas G. Jenkins , Andrew M. Chap , John R. Cary

In this paper, we introduce and discuss an exactly energy-conserving Particle-in-Cell method for arbitrary curvilinear coordinates. The flexibility provided by curvilinear coordinates enables the study of plasmas in complex-shaped domains…

Plasma Physics · Physics 2023-10-30 Joost Croonen , Luca Pezzini , Fabio Bacchini , Giovanni Lapenta
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